In my opinion, one should not get into the habit of equating Greek and Roman (English) letters. (There is no equivalent of $\psi$ or of $q$; $\lambda$ is a Lagrange multiplier but $\ell$ rarely is; $x$ is an unknown but $\xi$ is something special, etc etc.)
Searching for "h(kappa)" restricted to the Math StackExchange (or even not) does give the desired result.
There is a cost to having a search for Roman letters return results involving the "corresponding" Greek letter. Someone who really is looking for, say, Euler's number $e$ will be burdened by lots of unrelated results involving infinitesimals $\epsilon$.
You could put in something to the effect of: For the benefit of future searchers, the question is "What does H(k) mean?" But others might see that as obtrusive (by which I mean, I would see it as obtrusive). So I would recommend that you should reserve it for questions where you feel it is particularly likely that someone might search for the Roman letter in place of the Greek one, such as, as you say, those at the undergraduate or high school level.